Questions: Sampling by □ is a measurement in the amount of deviation from a set standard.

Transcript text: Sampling by $\square$ is a measurement in the amount of deviation from a set standard.

Solution

Step 1: Calculate the Mean

The mean $ \mu $ of the dataset is calculated as follows:

\[ \mu = \frac{\sum x_i}{n} = \frac{144}{8} = 18.0 \]

Step 2: Calculate the Variance

The variance $ \sigma^2 $ is computed using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} \]

Substituting the values, we find:

\[ \sigma^2 = 27.43 \]

Step 3: Calculate the Standard Deviation

The standard deviation $ \sigma $ is the square root of the variance:

\[ \sigma = \sqrt{27.43} = 5.24 \]

Sampling by variance is a measurement in the amount of deviation from a set standard. Thus, the final results are:

\[ \text{Variance: } \boxed{27.43} \] \[ \text{Standard Deviation: } \boxed{5.24} \]

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